Find the Rate of Change between each pair of points

The correct option C: r = √(√3)² + (√3)² = √6; θ  = arctan (1) = π/4.

The complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

The polar coordinates r (a radial coordinate) and in Cartesian space (the angular coordinate, generally termed as  polar angle),

x = rcosθ  .....(1)

y = rsinθ,  .....(2)

where is indeed the counterclockwise angle first from x-axis and r is the radial distance to the origin. Considering x and y,

r² = x² + y²  ...eq 3

θ  = arc tan (y/x)

Using the polar coordinates explanation from above, we can deduce that;

r² = x² + y²  .

r² = √3² + √3²  .

r = √(√3)² + (√3)²

and

θ  = arc tan (√3/√3) = arctan (1) = π/4.

Thus, the complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

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The compete question is attached.

Answer:

x = 3 and -2/3

Step-by-step explanation:

(6x - 18) (3x + 2) = 0

6x - 18 = 0

6x = 18

x = 3

3x + 2 = 0

3x = -2

x = -2/3

Answer:

Step-by-step explanation:

i think i answered another question by you but ill help anyways

ok so you are trying to check the fact that x=2 for both equations

for A. by using substitution

and B. by properties of Equality

A is easy you just substitute 2 into the x values in the given equations

it will look like

-3x+14=18-5x

-3(2)+14=18-5(2)

-6+14=18-10

8=8

and

2x=5-1/2x

2(2)=5-1(2)/2

4=5-2/2

4=5-1

4=4

so now we have proved that both x are eual to 2 by using substitution

i already answered b on a different question

$10.6375 she tip if she wants to give a 23% tip of the whole bill when  tab for the nice supper that Kristyn and her sister had was $ 46.25.

Given that,

The tab for the nice supper that Kristyn and her sister had was $ 46.25.

We have to find how much should she tip if she wants to give a 23% tip of the whole bill.

We know that,

The tab for the nice supper that Kristyn and her sister had was $ 46.25.

So,

23% tip of the whole bill is

=$ 46.25×23%

=10.6375

Therefore, $10.6375 she tip if she wants to give a 23% tip of the whole bill when  tab for the nice supper that Kristyn and her sister had was $ 46.25.

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The value of x in the equation x + 5 = 7 is 2

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is:

x + 5 = 7

Collect the like terms

x = 7 - 5

x = 2

Therefore, x is 2.

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Answer:

x = 2

Step-by-step explanation:

Given equation,

→ x + 5 = 7

Now the value of x will be,

→ x + 5 = 7

→ x + 5 - 5 = 7 - 5

→ [ x = 2 ]

Hence, the value of x is 2.

Answer:

Step-by-step explanation:

Plutonium is a radioactive element that is known to release large amounts of energy through the process of nuclear fission. When a nucleus of plutonium atom is split, it releases a tremendous amount of energy in the form of heat, light, and radiation. This energy is released through a chain reaction, in which the energy from one fission event is used to trigger the fission of additional atoms, releasing even more energy. The heat energy produced by plutonium can be harnessed and used in various ways, such as generating electricity or powering spacecraft.

It is important to note that the behavior of plutonium depicted in the movie "Martian" may be based on scientific concepts, but it may also include fictional elements and may not be entirely accurate or realistic. It is important to remember that fictional works are not necessarily scientifically accurate and should not be taken as fact.

The plutonium emit neutrons as a few of its nuclei spontaneously undergo nuclear fission, which is the reason behind the heat generation.

Given is a dug out plutonium.

Plutonium - 238, Pu - 240 and Pu - 242 emit neutrons as a few of their nuclei spontaneously undergo nuclear fission, albeit at a low rate. This is the reason why plutonium acts as a source of heat energy for Matt Damon and helped him save the fuel.

Therefore, the plutonium emit neutrons as a few of its nuclei spontaneously undergo nuclear fission, which is the reason behind the heat generation.

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The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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The percentile rank of score 71 on the test is 26.7 and The score of the 60th percentile on the test is 84.

The figure that a particular percentage falls within is referred to as the percentile. For instance, 80% of the kids in a group of 20 are shorter than you, and Ben is the fourth tallest.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

[tex]Percentile= n / N \times 100[/tex]

Here, n is the number of scores below 71 and N is the total number of scores,

Percentile = 4 / 15 × 100

Percentile = 0.267 × 100

Percentile = 26.7 percentile

Therefore, the percentile rank of score 71 on the test is 26.7

(B)

Substitute the value in the formula given below,

60 = n / 15 × 100

n / 15 = 60 / 100

n = 0.6 ×  15

n = 9

Thus, the 9th term here is 84,

Therefore, the score of the 60th percentile on the test is 84.

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The solution to the given simultaneous equations are;

x = 5/3 and y = 7/3

We are given the two simultaneous equations as;

x + y = 4  

y = 2x -1

Rearranging the second equation to have all the variables on one side gives; 2x - y = 1

Thus, we have the equations;

x + y = 4   ------(1)

2x - y = 1    -----(2)

Add eq 1 to eq 2 to get;

3x = 5

divide both sides by 3 using division property of equality to get;

x = 5/3

Put 5/3 for x in eq 1 to get;

⁵/₃ + y = 4

y = 4 - ⁵/₃

y = ⁷/₃

Thus, those are the solutions to the simultaneous equations.

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Answer:

To avoid consecutive b's, the string of b's must be divided into one or more groups of 1, 2, or 3 b's. There are a total of 5 + 1 = 6 possible places to insert the dividers to create these groups. For example, suppose we have a string of 7 b's and we insert dividers between the 3rd and 4th b's, and between the 5th and 6th b's. This would create the following groups of b's: bb|bb|b. In general, the number of possible ways to divide the string of b's into groups of 1, 2, or 3 b's is equal to the number of ways to insert 6 dividers into a string of 7 b's. This is equal to the number of ways to choose 6 of the 8 possible places to insert the dividers, which is equal to $\binom{8}{6} = 28$.

Since the 5 a's and the 1 c must be arranged in a specific order, there is only 1 way to arrange these letters. Therefore, the total number of words consisting of 5 letter a's, 7 letter b's, and 1 letter c is equal to $1 \times 28 = 28$.

Answer:

-----------------------------------------------

According to the question there are 7 'b' s  and we can't have them together. We assume more than two consecutive 'b' s contain two consecutive 'b' s and hence not considering any option of having 3, 4, 6 or 7 'b' s.

There is only one way to place 'b' s apart which leaves us with 6 gaps.

There are 5 + 1 = 6 other letters which is just the number to fill in the gaps between 7 'b' s.

We have only an option for 'c' to have any of the 6 gaps, it gives us 6 options and no other options for 'a' s.

Therefore in total we have 6 possible ways.

A quadrilateral whose diagonals do not always bisect each other is a rectangle.

A rectangle is a quadrilateral with four right angles. The diagonals of a rectangle are perpendicular to each other and bisect each other, but not all quadrilaterals with perpendicular diagonals and diagonals that bisect each other are rectangles. For example, a square is a type of quadrilateral with perpendicular diagonals and diagonals that bisect each other, but it has four congruent sides and four right angles, unlike a rectangle.

The word "rectangle" comes from the Latin words "rectus," meaning "right," and "angulus," meaning "angle." This reflects the fact that a rectangle has four right angles.

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Brust's votes equaled 2 times the sum of Pitt's votes and 400:

The total number of votes received was 2012:

Solve for P by substitution:

Find B:

Answer:

a)   Total # of votes:   B + P = 2012

     Brust vs Pitt:   B = 2(P + 400)

b)   1608 = votes for Brust

      404 = votes for Pitt

      Brust won by 1204 votes

Step-by-step explanation:

Given variables:

Given information:

Create a system of linear equations using the given variable and information:

Substitute the second equation into the first equation and solve for P:

⇒ 2(P + 400) + P = 2012

⇒ 2P + 800 = 2012

⇒ 3P = 1212

⇒ P = 404

Substitute the found value of P into the first equation and solve for B:

⇒ B + 404 = 2012

⇒ B = 1608

Therefore:

To find how many votes Brust won by, subtract the total number of votes for Pitt from the total votes for Brust:

⇒ 1608 - 404 = 1204

Answer:

The common ratio is 2.

The expression of log₄405 in terms of the logarithms of prime numbers is; 4 log₄3 + log₄ 5

One of the laws of logarithm is that;

log (a * b) = log a + log b

Now, we are given the logarithmic expression as; log₄405

We can express 405 in terms of prime numbers as;

405 = 81 * 5 = 3⁴ × 5

Thus, we have;

log₄405 =  log₄(3⁴ × 5)

Since log (a * b) = log a + log b, then;

log₄(3⁴ × 5) =  log₄3⁴ +  log₄ 5

= 4 log₄3 + log₄ 5

3 and 5 are prime numbers because they are divisible by only themselves or 1.

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1/2 is the scale factor from the cliff in the drawing to the actual cliff.

A scale factor is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller. The scale factor is 2 because the length of each of the sides has been multiplied by 2. If this is reversed: The scale factor is 1/2 because the length of each of the sides has been divided by 2.

A scale factor of 1/2 means that the new shape is half the size of the original shape.

Scale factor = Larger figure dimensions ÷ Smaller figure dimensions

The scale factor for scaling up is always greater than 1. Scaling down means that a larger figure is reduced to a smaller one. The scale factor of a dilated figure is denoted by 'r' or 'k'.

If the scale factor is more than 1, the image is enlarged.

If the scale factor is less than 1, the image is contracted.

If the scale factor is 1 (k = 1), the image remains the same.

The scale factor cannot be zero.

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The Answer is 38 seats for the 30th row! Because...

It is Adding up by 4 seats:)

Glad to help....

Mark me brainlyest ty!

Answer:

-2, 8/3

Step-by-step explanation:

You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...

 A = (1/2)(f(a) +f(4))(4 -a)

 = (1/2)((3a -1) +(3·4 -1))(4 -a)

 = (1/2)(3a +10)(4 -a)

We want this area to be 12, so we can substitute that value for A and solve for "a".

 12 = (1/2)(3a +10)(4 -a)

24 = (3a +10)(4 -a) = -3a² +2a +40

 3a² -2a -16 = 0 . . . . . . subtract the right side

 (3a -8)(a +2) = 0 . . . . . factor

Values of "a" that make these factors zero are ...

 a = 8/3, a = -2

The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.

Alternate solution

The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.

If points d and f are on side ab and points e and g are on side ac then line segments de and fg are parallel

What are parallel lines?

Parallel lines are those lines that do not meet at any point. If we draw a triangle ABC and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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Explanation:

Use the trigonometric ratio cosine.

Remember that [tex]\cos(x) = \dfrac{\textrm{adjacent}}{\textrm{hypotenuse}}[/tex].

So, we can construct the following equation using the given triangle:

[tex]\cos(23\textdegree)=\dfrac{11}{x}[/tex]

And solve for x. First, take the reciprocal of both sides (flip both sides).

[tex]\dfrac{\cos(23\textdegree)}{1}=\dfrac{11}{x}[/tex]

        ↓

[tex]\dfrac{1}{\cos(23\textdegree)}=\dfrac{x}{11}[/tex]

Then, multiply both sides by 11.

[tex]11\cdot\left(\dfrac{1}{\cos(23\textdegree)}\right)=\left(\dfrac{x}{11}\right) \cdot 11[/tex]

[tex]\dfrac{11}{\cos(23 \textdegree)} = x[/tex]

[tex]x = \dfrac{11}{\cos(23 \textdegree)}[/tex]

Finally, plug this fraction into your calculator as 11/cos(23) to get approximately 11.95.

Also, make sure that your calculator's mode is degrees, NOT radians.

When the sum of 5 and y is greater than or equal to -19, the inequality is y ≥ - 24.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since the sum of 5 and y is greater than or equal to -19, this will be:

5 + y ≥ - 19

y ≥-19 - 5.

y ≥ - 24

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Complete question

The sum of 5 and y is greater than or equal to -19. Express the inequality.

Answer:

y=16-3x

Step-by-step explanation:

change in x /change in y

Two angles are called complementary when their measures add up to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Complementary angles add up to 90°- example: 15° & 75° are complimentary

For example:

Suppose if one angle is x then the other angle will be 90° – x.

Now, to find the complement of 2x + 52°, subtract the given angle from 90 degrees.

90o –  (2x + 52o) =  90o – 2x – 52o  = -2x + 38o

The complement of 2x + 52o is 38o – 2x.

Supplementary angles add up to 180°- example: 50° & 130° are supplementary

if the two angles form a linear angle, such that, if one angle is x, then the other angle is 180° – x

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Según el método de diferenciales, el cambio aproximado del volumen del prisma es aproximadamente igual a 60 centímetros cúbicos.

Las diferenciales son una generalización del concepto matemático de cambio para funciones de una o más variables. Las versiones de una sola variable involucran derivadas ordinarias, mientras las versiones multivariables utilizan derivadas parciales.

El volumen del prisma es igual al producto del área de la base (A), en centímetros cuadrados, y la altura (h), en centímetros.

V(h, A) = h · A

El área de la base es igual al área de un cuadrado, es decir:

A(x) = x²

Donde x es la longitud del lado, en centímetros.

Según el enunciado, la altura del prisma es constante, mientras la longitud del lado de la base es una variable. En consecuencia, tenemos un diferencial que emplea derivadas ordinarias, esto es:

ΔV = (dV / dx) · Δx

V(x) = 15 · x²

dV / dx = 30 · x

Si sabemos que x = 10 cm y Δx = 0.02 cm, entonces el cambio en el volumen del prisma es:

ΔV = 30 · (10 cm)² · (0.02 cm)

ΔV = 60 cm³

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Answer:

19x20

Step-by-step explanation:

The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width of the rectangle. In this case, we are given that the area of the rectangle is 380 square meters and that the length and width of the rectangle are consecutive integers.

We can use this information to create a system of equations to solve for the length and width of the rectangle. Let l be the length of the rectangle and w be the width of the rectangle. Since the length and width of the rectangle are consecutive integers, we have:

l = w + 1

Substituting this equation into the formula for the area of the rectangle, we get:

A = l * w

= (w + 1) * w

= w² + w

Since the area of the rectangle is given as 380 square meters, we can set this equation equal to 380 and solve for w:

w² + w = 380

To solve for w, we can use the quadratic formula, which is given by:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation, and x is the solution. Substituting the values of a, b, and c into the formula and simplifying, we get:

w = (-1 ± √(1² - 4(1)(380))) / (2(1))

= (-1 ± √(-1519)) / 2

Since the length and width of the rectangle must be positive integers, we can ignore the negative solution and only consider the positive solution. Therefore, the width of the rectangle is 19.

To find the length of the rectangle, we can use the equation l = w + 1 that we derived earlier. Substituting the value of w into this equation, we get:

l = w + 1

= 19 + 1

= 20

Therefore, the length of the rectangle is 20 and the width of the rectangle is 19. The dimensions of the rectangle are 20 x 19.

The solution of the z-score of the standard deviation is [tex]0.5[/tex].

What is the standard deviation?

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Here given that,

The weight for twelve month old baby boys are normally distributed wih the mean [tex]22.5[/tex] pounds and a standard deviation of [tex]2.2[/tex] pounds.

Here, [tex]mean=22.5[/tex] , standard deviation [tex]=2.2[/tex]

z-score = (Blood pressure reading - mean)/standard deviation

[tex]=\frac{23.6=22.5}{2.2}\\\\=\frac{1.1}{2.2}\\\\=0.5[/tex]

Hence, the percentage is [tex]0.5[/tex].

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Answer:

A Yard

Step-by-step explanation:

Yards are 36 inches and feet are 12

Electric company charges 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400.

Electric companies charge customers for the amount of energy they consume, measured in kilowatt-hours (kWh). The cost for each kWh can vary depending on the amount of energy consumed. An electric company may charge 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400. The higher rate for higher usage reflects the fact that larger consumers of electricity tend to drive up the cost of production and distribution for the company. In addition, electric companies may offer discounts to customers who use more than a certain amount of electricity each month, encouraging conservation and helping to reduce costs.

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Complete Question  is

Economic The table how cot in dollar charged by an electric company for

variou amount of energy in kilowatt-hour

Kilowatt-Hour  Cost in Dollars

0-50 .            7.50

50-100.          10.00

100-200.      13.50

200-300.       18.50

300-400.       20.00

400+.                25.00

The congruent angles of the statements are;

∠1 + ∠3 = 180° by Vertical angles theorem.

∠5 + ∠6 = 180° by Linear pair theorem.

∠1 + ∠3 = ∠5 + ∠6 by both are supplementary angles.

∠3 = ∠6 by consecutive interior angles

∠1 = ∠5 by corresponding angles.

We want to prove that ∠1 = ∠5.

Corresponding angles; When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.

From the given question, we see that;

∠1 + ∠3 = 180°: This is because ∠1 and ∠3 are vertical angles by the vertical angles theorem.

∠5 + ∠6 = 180°: This is because ∠5 and ∠6 are linear pairs by the Linear pair theorem.

∠1 + ∠3 = ∠5 + ∠6 ; 180° = 180° ; Both are supplementary angles.

∠3 = ∠6 ; Consecutive interior angles

Now, ∠1 = ∠5, Corresponding angles.

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Based on the storage capacity, Lunanne's car has 13 gallons of gas left in the tank.

Storage capacity of car = distance covered in total ÷ distance covered in one gallon

Keep the values in formula to find the storage capacity of car

Storage capacity of car = 675 ÷ 45

Performing division on Right Hand Side of the equation

Storage capacity of car = 15 gallons

Amount of gas left in tank = 15 - 2

Performing subtraction on Right Hand Side of the equation

Amount of gas left in tank = 13 gallons

Hence, 13 gallons of gas is left.

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Answer:

To solve this equation, we need to perform the operations in the correct order according to the order of operations. The order of operations is a set of rules for determining the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Applying the order of operations to the given equation, we first need to evaluate the expression inside the parentheses, which is 3(x - 6). To do this, we need to subtract 6 from x, which gives us 3(x - 6) = 3(11 - 6) = 3(5) = 15. Next, we need to multiply the result of this operation by 3, which gives us 3 * 15 = 45. Therefore, the final result of the equation is 45.

Here is how you can solve the equation step by step:

1. Evaluate the expression inside the parentheses: 3(x - 6) = 3(11 - 6) = 3(5) = 15

2. Multiply the result of the previous step by 3: 3 * 15 = 45

Therefore, the final result of the equation is 45.

Step-by-step explanation: